Notebook[{
Cell["Gamma matrices (Dirac algebra) example", \
"Section",ExpressionUUID->"1260ef40-5d72-4943-a19b-252cee3625d5"],

Cell[CellGroupData[{

Cell[TextData[{
 "Author: \[Copyright] Leo C. Stein (",
 ButtonBox["leo.stein@gmail.com",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["mailto:leo.stein@gmail.com"], None},
  ButtonNote->"mailto:leo.stein@gmail.com"],
 ")\nDate: 2018.02.24; simplified 2018.03.28\nTODO: No treatment of Dagger or \
algebra trace."
}], "Subtitle",ExpressionUUID->"9fec8a2f-1cfa-4acc-84ec-a7153a5b3284"],

Cell[CellGroupData[{

Cell["0. Overhead", \
"Subsubsection",ExpressionUUID->"d19dc23e-a35a-4df7-8f2f-b54e2f17231b"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Needs", "[", "\"\<xAct`xTensor`\>\"", "]"}]], "Input",
 CellLabel->"In[1]:=",ExpressionUUID->"c008a5f4-ebf4-49d2-a924-11f1654d1408"],

Cell[CellGroupData[{

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"a126bd8c-540a-4f92-ab19-a750d944cddf"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Package xAct`xPerm`  version \"\>", 
   "\[InvisibleSpace]", "\<\"1.2.3\"\>", "\[InvisibleSpace]", "\<\", \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{"2015", ",", "8", ",", "23"}], "}"}]}],
  SequenceForm["Package xAct`xPerm`  version ", "1.2.3", ", ", {2015, 8, 23}],
  
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"9909db58-b61b-445a-9fa9-0d197ad09ac7"],

Cell[BoxData["\<\"CopyRight (C) 2003-2018, Jose M. Martin-Garcia, under the \
General Public License.\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"95dfabfd-1899-43ef-b3da-d0fa442436d5"],

Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"b7165fd7-775b-43b9-b46f-9351827d74a6"],

Cell[BoxData["\<\"Connection established.\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"483447d4-d14b-4001-80a9-fccd86a96eeb"],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"e30f0249-1949-494d-a066-282f31bf296e"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Package xAct`xTensor`  version \"\>", 
   "\[InvisibleSpace]", "\<\"1.1.3\"\>", "\[InvisibleSpace]", "\<\", \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{"2018", ",", "2", ",", "28"}], "}"}]}],
  SequenceForm[
  "Package xAct`xTensor`  version ", "1.1.3", ", ", {2018, 2, 28}],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"7fa88893-5bc5-4515-99ed-2b1adc5f63e7"],

Cell[BoxData["\<\"CopyRight (C) 2002-2018, Jose M. Martin-Garcia, under the \
General Public License.\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"f1add364-33de-460c-9d53-76c56f2d6954"],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"f9adb165-07ee-4d2b-b04f-31c13f726927"],

Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \
details type Disclaimer[]. This is free software, and you are welcome to \
redistribute it under certain conditions. See the General Public License for \
details.\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"b3d7fc9b-32b5-4944-8486-0a1b8b2d108d"],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[1]:=",ExpressionUUID->"a9a1295f-5125-4441-84a0-180a8c4e6ab7"]
}, Open  ]]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"$PrePrint", "=", "ScreenDollarIndices"}], ";"}]], "Input",
 CellLabel->"In[2]:=",ExpressionUUID->"8c9a25b0-7ad3-48a0-afdd-f1510bc94519"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefManifold", "[", 
  RowBox[{"M", ",", "4", ",", 
   RowBox[{"Complement", "[", 
    RowBox[{
     RowBox[{"IndexRange", "[", 
      RowBox[{"a", ",", "q"}], "]"}], ",", 
     RowBox[{"{", "g", "}"}]}], "]"}]}], "]"}]], "Input",
 CellLabel->"In[3]:=",ExpressionUUID->"ba13ee4f-dbe6-45cd-9ed3-c9f9c016b3cf"],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefManifold", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"manifold \"\>", "\[InvisibleSpace]", "M", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefManifold, ": Defining ", "manifold ", $CellContext`M,
    ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[3]:=",ExpressionUUID->"7a964000-12a7-4b0a-96d6-2550de464334"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "TangentM", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefVBundle, ": Defining ", 
   "vbundle ", $CellContext`TangentM, ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[3]:=",ExpressionUUID->"5245ef85-3483-425e-a8a4-120898b9a609"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefMetric", "[", 
  RowBox[{
   RowBox[{"-", "1"}], ",", 
   RowBox[{"g", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}]}], "]"}], ",", "PD", ",", 
   RowBox[{"FlatMetric", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellLabel->"In[4]:=",ExpressionUUID->"ffe91ee0-6f16-4188-986c-7a5b9c3ebf2f"],

Cell[BoxData[
 TemplateBox[{
  "DefMetric","error",
   "\"\\!\\(\\*RowBox[{\\\"\\\\\\\"Using standard {,, \[PartialD]} as symbols \
for PD.\\\\\\\"\\\"}]\\)\"",2,4,1,29891062705255529835,"Local",
   "xAct`xTensor`DefMetric"},
  "MessageTemplate2"]], "Message", "MSG",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"ac5bde81-b454-4925-b9e9-c57eb68a5eec"],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric metric tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"g", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric metric tensor ", 
   $CellContext`g[-$CellContext`a, -$CellContext`b], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"b43151ef-9437-4501-b20f-153b8081793a"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"antisymmetric tensor \"\>", "\[InvisibleSpace]", 
   
   RowBox[{"epsilong", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}], ",", 
     RowBox[{"-", "c"}], ",", 
     RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "antisymmetric tensor ", 
   $CellContext`epsilong[-$CellContext`a, -$CellContext`b, -$CellContext`c, \
-$CellContext`d], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"ac6ca56f-1630-4646-97ae-6b28692ed3ad"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tetrametric \"\>", "\[InvisibleSpace]", 
   RowBox[{"Tetrag", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}], ",", 
     RowBox[{"-", "c"}], ",", 
     RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tetrametric ", 
   $CellContext`Tetrag[-$CellContext`a, -$CellContext`b, -$CellContext`c, \
-$CellContext`d], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"99ab5aa9-78e0-4a80-a658-b06d9dee67ec"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tetrametric \"\>", "\[InvisibleSpace]", 
   RowBox[{"Tetrag\[Dagger]", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}], ",", 
     RowBox[{"-", "c"}], ",", 
     RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tetrametric ", 
   $CellContext`Tetrag\[Dagger][-$CellContext`a, -$CellContext`b, \
-$CellContext`c, -$CellContext`d], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"85c79457-11c4-4f97-b0d5-276915e37267"],

Cell[BoxData["\<\"** DefMetric: Associating fiducial flat derivative PD to \
metric.\"\>"], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"2c0cd7eb-652f-472f-a479-9d8fe5418976"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"weight +2 density \"\>", "\[InvisibleSpace]", 
   RowBox[{"Detg", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"Determinant.\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "weight +2 density ", 
   $CellContext`Detg[], ". ", "Determinant."],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"9073cabb-492a-46ba-bf1f-808b743e24e8"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["1. Create the algebra", \
"Subsubsection",ExpressionUUID->"a6308d03-e21c-4c73-b4fb-305901912982"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "DefProduct", "]"}]], "Input",
 CellLabel->"In[5]:=",ExpressionUUID->"b66a7b66-0b77-4028-b23b-eaef840c3a58"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"AssociativeProductQ", "\[Rule]", "False"}], ",", 
   RowBox[{"IdentityElementOfProduct", "\[Rule]", "None"}], ",", 
   RowBox[{"CommutativityOfProduct", "\[Rule]", "None"}], ",", 
   RowBox[{"GradedProductQ", "\[Rule]", "False"}], ",", 
   RowBox[{"GradeOfProduct", "\[Rule]", "0"}], ",", 
   RowBox[{"ScalarsOfProduct", "\[Rule]", "NumericQ"}], ",", 
   RowBox[{"DefineCommutator", "\[Rule]", "False"}], ",", 
   RowBox[{"xSortOrder", "\[Rule]", "Automatic"}], ",", 
   RowBox[{"Master", "\[Rule]", "Null"}], ",", 
   RowBox[{"PrintAs", "\[Rule]", "\<\"\[Diamond]\"\>"}], ",", 
   RowBox[{"ProtectNewSymbol", "\[RuleDelayed]", "$ProtectNewSymbols"}], ",", 
   
   RowBox[{"DefInfo", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"\<\"product\"\>", ",", "\<\"\"\>"}], "}"}]}]}], "}"}]], "Output",
 CellLabel->"Out[5]=",ExpressionUUID->"47238db7-91cc-4a92-8444-b6e811c2f8e5"]
}, Open  ]],

Cell["\<\
Because of the way DefProduct works, we need to already have a definition for \
AlgElementQ[1]. Another perfectly valid approach is to create an element id[] \
to be the identity in the algbera.\
\>", "Text",ExpressionUUID->"4e48b4dc-199c-4d11-81c0-a59aae566fc5"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"AlgElementQ", "[", "1", "]"}], "=", "False"}], ";"}]], "Input",
 CellLabel->"In[6]:=",ExpressionUUID->"e6df5496-0081-4155-a5b0-0b857289050b"],

Cell["\<\
I name this product AP for \[OpenCurlyQuote]algebra \
product\[CloseCurlyQuote]. We also get (super-)commutators out of this. We \
could do this without making the algebra graded, and just being explicit \
about Anticommutator[] instead of Supercommutator[].\
\>", "Text",ExpressionUUID->"cd913591-f952-40d4-93f6-0eb91a6a5c77"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefProduct", "[", 
  RowBox[{"AP", ",", "\[IndentingNewLine]", 
   RowBox[{"AssociativeProductQ", "\[Rule]", "True"}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"IdentityElementOfProduct", "\[Rule]", "1"}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"GradedProductQ", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", 
   
   RowBox[{"ScalarsOfProduct", "\[Rule]", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"!", 
       RowBox[{"AlgElementQ", "[", "#", "]"}]}], "&"}], ")"}]}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"DefineCommutator", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellLabel->"In[7]:=",ExpressionUUID->"52ca07fa-8dc4-4aad-9ab8-2ef2b4bfc098"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefProduct", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"product \"\>", "\[InvisibleSpace]", "AP", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefProduct, ": Defining ", "product ", $CellContext`AP, 
   ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[7]:=",ExpressionUUID->"c3533a8d-078d-4933-9453-025b96711629"]
}, Open  ]],

Cell["\<\
Define our gamma elements, and give them odd grades under this product, so \
that the supercommutator is the anticommutator.
NOTE: These should really be complex, but I ignore it in this notebook.\
\>", "Text",ExpressionUUID->"9437f290-6d1e-41d3-8b2b-e1c55751ae94"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefTensor", "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "i", "]"}], ",", "M", ",", 
   RowBox[{"GradeOfTensor", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"AP", "\[Rule]", "1"}], "}"}]}]}], "]"}]], "Input",
 CellLabel->"In[8]:=",ExpressionUUID->"24c88dca-4fdc-4f90-b480-05450c3c6d01"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"\[Gamma]", "[", "i", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`\[Gamma][$CellContext`i], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[8]:=",ExpressionUUID->"6deaaf30-5894-413d-b8fb-6e33a76088bc"]
}, Open  ]],

Cell["\<\
List of elements in the algebra. How to test for being in the algebra. So far \
I\[CloseCurlyQuote]ve only needed definitions for individual tensors and \
products thereof. TODO: What else is needed here?\
\>", "Text",ExpressionUUID->"3fb86412-74d6-4e4f-aaba-71ffa0d9413c"],

Cell[BoxData[
 RowBox[{
  RowBox[{"AlgebraElements", "=", 
   RowBox[{"{", "\[Gamma]", "}"}]}], ";"}]], "Input",
 CellLabel->"In[9]:=",ExpressionUUID->"dfe018f9-5a68-4e3d-80f6-7f128a7758b6"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"AlgElementQ", "[", 
   RowBox[{
    RowBox[{"t_", "?", "xTensorQ"}], "[", "___", "]"}], "]"}], ":=", 
  RowBox[{"!", 
   RowBox[{"FreeQ", "[", 
    RowBox[{"AlgebraElements", ",", "t"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"AlgElementQ", "[", 
   RowBox[{"HoldPattern", "[", 
    RowBox[{"Times", "[", "factors___", "]"}], "]"}], "]"}], ":=", 
  RowBox[{"Or", "@@", 
   RowBox[{"(", 
    RowBox[{"AlgElementQ", "/@", 
     RowBox[{"{", "factors", "}"}]}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"AlgElementQ", "[", 
   RowBox[{"HoldPattern", "[", 
    RowBox[{"AP", "[", "factors___", "]"}], "]"}], "]"}], ":=", 
  RowBox[{"Or", "@@", 
   RowBox[{"(", 
    RowBox[{"AlgElementQ", "/@", 
     RowBox[{"{", "factors", "}"}]}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"AlgElementQ", "[", "_", "]"}], "=", "False"}], ";"}]}], "Input",
 CellLabel->
  "In[10]:=",ExpressionUUID->"1d97f44e-0046-4b00-8d71-3e6032172cbb"]
}, Closed]],

Cell[CellGroupData[{

Cell["2. Examples", \
"Subsubsection",ExpressionUUID->"511dfa19-ef95-4c8a-85fa-a9ebe9cdbd12"],

Cell["\<\
Here are some products. Notice that since there is no particular symmetry, \
the canonicalizer doesn\[CloseCurlyQuote]t do anything in particular.\
\>", "Text",ExpressionUUID->"2db29be7-c636-4aa8-b306-5aa2f8db196c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Permutations", "[", 
  RowBox[{"{", 
   RowBox[{"i", ",", "j", ",", "k"}], "}"}], "]"}]], "Input",
 CellLabel->"In[14]:=",ExpressionUUID->"f8343d5a-60fb-4e0d-8f69-6cb61eabdfb7"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"i", ",", "j", ",", "k"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"i", ",", "k", ",", "j"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"j", ",", "i", ",", "k"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"j", ",", "k", ",", "i"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", "i", ",", "j"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", "j", ",", "i"}], "}"}]}], "}"}]], "Output",
 CellLabel->
  "Out[14]=",ExpressionUUID->"af6a92b1-abc7-4ba7-863f-970e45a24682"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"{", 
  RowBox[{
   RowBox[{"AP", "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "i", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "j", "]"}]}], "]"}], ",", 
   RowBox[{"AP", "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "j", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "i", "]"}]}], "]"}]}], 
  "}"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "ToCanonical"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"AP", "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", 
      RowBox[{"#", "[", 
       RowBox[{"[", "1", "]"}], "]"}], "]"}], ",", 
     RowBox[{"\[Gamma]", "[", 
      RowBox[{"#", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "]"}], ",", 
     RowBox[{"\[Gamma]", "[", 
      RowBox[{"#", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "]"}]}], "]"}], "&"}], "/@", 
  RowBox[{"Permutations", "[", 
   RowBox[{"{", 
    RowBox[{"i", ",", "j", ",", "k"}], "}"}], 
   "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "ToCanonical"}]}], "Input",
 CellLabel->"In[15]:=",ExpressionUUID->"48dc59db-78ee-43b8-90e8-0feb7b4c1547"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[15]=",ExpressionUUID->"af0c329f-163c-4264-8438-fd81823ab6c5"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[16]=",ExpressionUUID->"b576fc25-d186-4336-aa2e-fcd9b1aeb568"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`k]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`k]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[17]=",ExpressionUUID->"4baa1ec4-0eed-4184-bfaf-b0f483a949a7"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`k]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`k]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"k"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`k],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`k], 
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->
  "Out[18]=",ExpressionUUID->"5d9d25ae-9be7-49bd-ba7e-37997f8e987f"]
}, Open  ]],

Cell["\<\
The canonicalizer already understands the symmetry properties of Commutator:\
\>", "Text",ExpressionUUID->"484fa3d7-e4e8-424a-bc3d-97ab68f20fc4"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"{", 
  RowBox[{
   RowBox[{"AP", "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "i", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "j", "]"}]}], "]"}], ",", 
   RowBox[{
    RowBox[{"Commutator", "[", "AP", "]"}], "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "i", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "j", "]"}]}], "]"}], ",", 
   RowBox[{
    RowBox[{"Commutator", "[", "AP", "]"}], "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "j", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "i", "]"}]}], "]"}]}], 
  "}"}], "\[IndentingNewLine]", 
 RowBox[{"SymmetryOf", "/@", "%"}]}], "Input",
 CellLabel->"In[19]:=",ExpressionUUID->"30dc851f-f209-4047-af25-9ed1c83d2724"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"i"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`i],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"j"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`j],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"[", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Commutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"[", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], "]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Commutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`j], 
     $CellContext`\[Gamma][$CellContext`i]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[19]=",ExpressionUUID->"0065a321-8c94-417b-a0db-82ed254313e2"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"Symmetry", "[", 
    RowBox[{"2", ",", 
     RowBox[{
      RowBox[{"(", 
       TagBox[
        TooltipBox[
         UnderscriptBox["AP", "_"],
         RowBox[{"\"VerbatimProduct\"", "[", "AP", "]"}]],
        #& ], ")"}], "[", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"\[FilledCircle]1"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         xAct`xTensor`Private`slot[1]],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"\[FilledCircle]2"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         xAct`xTensor`Private`slot[2]],
        Editable->False]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"\<\"\[FilledCircle]1\"\>", "\[Rule]", "i"}], ",", 
       RowBox[{"\<\"\[FilledCircle]2\"\>", "\[Rule]", "j"}]}], "}"}], ",", 
     RowBox[{"StrongGenSet", "[", 
      RowBox[{
       RowBox[{"{", "}"}], ",", 
       RowBox[{"GenSet", "[", "]"}]}], "]"}]}], "]"}], ",", 
   RowBox[{"Symmetry", "[", 
    RowBox[{"2", ",", 
     RowBox[{
      RowBox[{"(", 
       TagBox[
        TooltipBox[
         UnderscriptBox[
          RowBox[{"Commutator", "[", "AP", "]"}], "_"],
         RowBox[{"\"VerbatimProduct\"", "[", 
           RowBox[{"Commutator", "[", "AP", "]"}], "]"}]],
        #& ], ")"}], "[", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"\[FilledCircle]1"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         xAct`xTensor`Private`slot[1]],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"\[FilledCircle]2"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         xAct`xTensor`Private`slot[2]],
        Editable->False]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"\<\"\[FilledCircle]1\"\>", "\[Rule]", "i"}], ",", 
       RowBox[{"\<\"\[FilledCircle]2\"\>", "\[Rule]", "j"}]}], "}"}], ",", 
     RowBox[{"StrongGenSet", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "2"}], "}"}], ",", 
       RowBox[{"GenSet", "[", 
        InterpretationBox[
         StyleBox[
          RowBox[{"-", 
           RowBox[{"(", "1", ",", "2", ")"}]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         -xAct`xPerm`Cycles[{1, 2}],
         Editable->False], "]"}]}], "]"}]}], "]"}], ",", 
   RowBox[{"Symmetry", "[", 
    RowBox[{"2", ",", 
     RowBox[{
      RowBox[{"(", 
       TagBox[
        TooltipBox[
         UnderscriptBox["Times", "_"],
         RowBox[{"\"VerbatimProduct\"", "[", "Times", "]"}]],
        #& ], ")"}], "[", 
      RowBox[{
       RowBox[{"-", "1"}], ",", 
       RowBox[{
        RowBox[{"(", 
         TagBox[
          TooltipBox[
           UnderscriptBox[
            RowBox[{"Commutator", "[", "AP", "]"}], "_"],
           RowBox[{"\"VerbatimProduct\"", "[", 
             RowBox[{"Commutator", "[", "AP", "]"}], "]"}]],
          #& ], ")"}], "[", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"\[FilledCircle]1"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][
           xAct`xTensor`Private`slot[1]],
          Editable->False], ",", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"\[FilledCircle]2"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][
           xAct`xTensor`Private`slot[2]],
          Editable->False]}], "]"}]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"\<\"\[FilledCircle]1\"\>", "\[Rule]", "i"}], ",", 
       RowBox[{"\<\"\[FilledCircle]2\"\>", "\[Rule]", "j"}]}], "}"}], ",", 
     RowBox[{"StrongGenSet", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "2"}], "}"}], ",", 
       RowBox[{"GenSet", "[", 
        InterpretationBox[
         StyleBox[
          RowBox[{"-", 
           RowBox[{"(", "1", ",", "2", ")"}]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         -xAct`xPerm`Cycles[{1, 2}],
         Editable->False], "]"}]}], "]"}]}], "]"}]}], "}"}]], "Output",
 CellLabel->
  "Out[20]=",ExpressionUUID->"e09b417b-89a4-4423-bb23-471ffdd48941"]
}, Open  ]],

Cell["\<\
All the (anti-,super-)commutators we can form. Note that canonicalization \
already works here (because SymmetryOf works as above).\
\>", "Text",ExpressionUUID->"d08048fe-d0ce-47de-ab39-8b05f3e85a0b"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"#1", "[", "AP", "]"}], "[", 
      RowBox[{
       RowBox[{"#2", "[", "i", "]"}], ",", 
       RowBox[{"#3", "[", "j", "]"}]}], "]"}], "&"}], ",", 
    RowBox[{"{", 
     RowBox[{"Commutator", ",", "Anticommutator", ",", "Supercommutator"}], 
     "}"}], ",", "AlgebraElements", ",", "AlgebraElements"}], "]"}], "//", 
  "Flatten"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "ToCanonical"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "ExpandCommutator"}]}], "Input",
 CellLabel->"In[21]:=",ExpressionUUID->"c6c6c7e4-c0ee-475f-98af-6769c2689556"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"[", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Commutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"{", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "}"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Anticommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"\[LeftDoubleBracket]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Supercommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[21]=",ExpressionUUID->"9474e4f8-9df8-4738-bafa-a1231bff0ce3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"[", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Commutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"{", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "}"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Anticommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False], ",", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"\[LeftDoubleBracket]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Supercommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     $CellContext`\[Gamma][$CellContext`j]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[22]=",ExpressionUUID->"75606708-c31b-4179-b3ce-9ada952f6637"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`i], 
      $CellContext`\[Gamma][$CellContext`j]],
     Editable->False], "-", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`j], 
      $CellContext`\[Gamma][$CellContext`i]],
     Editable->False]}], ",", 
   RowBox[{
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`i], 
      $CellContext`\[Gamma][$CellContext`j]],
     Editable->False], "+", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`j], 
      $CellContext`\[Gamma][$CellContext`i]],
     Editable->False]}], ",", 
   RowBox[{
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`i], 
      $CellContext`\[Gamma][$CellContext`j]],
     Editable->False], "+", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`j], 
      $CellContext`\[Gamma][$CellContext`i]],
     Editable->False]}]}], "}"}]], "Output",
 CellLabel->
  "Out[23]=",ExpressionUUID->"80430370-b1e1-43d8-adaa-d017d92b4bd8"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["3. (Super) Jacobi identity", \
"Subsubsection",ExpressionUUID->"7d1cdfd4-925b-49ca-b40a-3803c94c65e7"],

Cell["\<\
Actually just valid no matter what we do for the structure of the algebra. \
The even-even-even sector is just the ordinary Jacobi identity\
\>", "Text",ExpressionUUID->"0fdaab17-c726-4def-993e-a395b9a73e93"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Jac", "[", 
    RowBox[{"p_", "?", "ProductQ"}], "]"}], "[", 
   RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"sc", "=", 
      RowBox[{"Supercommutator", "[", "p", "]"}]}], "}"}], ",", 
    "\[IndentingNewLine]", 
    RowBox[{"3", 
     RowBox[{"Cyclize", "[", 
      RowBox[{
       RowBox[{"sc", "[", 
        RowBox[{"a", ",", 
         RowBox[{"sc", "[", 
          RowBox[{"b", ",", "c"}], "]"}]}], "]"}], ",", 
       RowBox[{"{", 
        RowBox[{"a", ",", "b", ",", "c"}], "}"}]}], "]"}]}]}], 
   "]"}]}]], "Input",
 CellLabel->"In[24]:=",ExpressionUUID->"75ecb135-ed99-4dc2-86af-2c14549c0441"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"Jac", "[", "AP", "]"}], "[", 
      RowBox[{
       RowBox[{"#1", "[", "i", "]"}], ",", 
       RowBox[{"#2", "[", "j", "]"}], ",", 
       RowBox[{"#3", "[", "k", "]"}]}], "]"}], "&"}], ",", "AlgebraElements", 
    ",", "AlgebraElements", ",", "AlgebraElements"}], "]"}], "//", 
  "Flatten"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "ExpandCommutator"}]}], "Input",
 CellLabel->"In[25]:=",ExpressionUUID->"be9762d6-8dcb-4a85-bd34-8d03152bfb53"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"\[LeftDoubleBracket]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[
         SubscriptBox[
          RowBox[{"\[LeftDoubleBracket]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], ",", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"k"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`k],
            Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xTensor`Supercommutator[$CellContext`AP][
         $CellContext`\[Gamma][$CellContext`j], 
         $CellContext`\[Gamma][$CellContext`k]],
        Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Supercommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`i], 
     xAct`xTensor`Supercommutator[$CellContext`AP][
      $CellContext`\[Gamma][$CellContext`j], 
      $CellContext`\[Gamma][$CellContext`k]]],
    Editable->False], "+", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"\[LeftDoubleBracket]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[
         SubscriptBox[
          RowBox[{"\[LeftDoubleBracket]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"k"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`k],
            Editable->False], ",", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xTensor`Supercommutator[$CellContext`AP][
         $CellContext`\[Gamma][$CellContext`k], 
         $CellContext`\[Gamma][$CellContext`i]],
        Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Supercommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`j], 
     xAct`xTensor`Supercommutator[$CellContext`AP][
      $CellContext`\[Gamma][$CellContext`k], 
      $CellContext`\[Gamma][$CellContext`i]]],
    Editable->False], "+", 
   InterpretationBox[
    StyleBox[
     SubscriptBox[
      RowBox[{"\[LeftDoubleBracket]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"k"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`k],
        Editable->False], ",", 
       InterpretationBox[
        StyleBox[
         SubscriptBox[
          RowBox[{"\[LeftDoubleBracket]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], ",", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xTensor`Supercommutator[$CellContext`AP][
         $CellContext`\[Gamma][$CellContext`i], 
         $CellContext`\[Gamma][$CellContext`j]],
        Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xTensor`Supercommutator[$CellContext`AP][
     $CellContext`\[Gamma][$CellContext`k], 
     xAct`xTensor`Supercommutator[$CellContext`AP][
      $CellContext`\[Gamma][$CellContext`i], 
      $CellContext`\[Gamma][$CellContext`j]]],
    Editable->False]}], "}"}]], "Output",
 CellLabel->"Out[25]=",ExpressionUUID->"e4634241-6c61-431c-9691-9f79a5412fde"],

Cell[BoxData[
 RowBox[{"{", "0", "}"}]], "Output",
 CellLabel->
  "Out[26]=",ExpressionUUID->"59420d4a-f7d8-42fb-81fa-ecadc86da511"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["4. Input the algebra\[CloseCurlyQuote]s structure", \
"Subsubsection",ExpressionUUID->"a67e44dc-7879-4843-b120-89259920270a"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"AlgebraStructure", "[", 
   RowBox[{"\[Gamma]", ",", "\[Gamma]"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Supercommutator", "[", "AP", "]"}], "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "i", "]"}], ",", 
     RowBox[{"\[Gamma]", "[", "j", "]"}]}], "]"}], "\[Equal]", 
   RowBox[{"2", 
    RowBox[{"g", "[", 
     RowBox[{"i", ",", "j"}], "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{"SetAttributes", "[", 
  RowBox[{"AlgebraStructure", ",", "Orderless"}], "]"}]}], "Input",
 CellLabel->"In[27]:=",ExpressionUUID->"8ea38443-7275-4a04-839a-f3cfd1b18710"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
   "AlgebraStructure", ",", "AlgebraElements", ",", "AlgebraElements"}], 
   "]"}], "//", "TableForm"}]], "Input",
 CellLabel->"In[29]:=",ExpressionUUID->"99af7ff7-650d-41f9-a7bc-60d26c9e2870"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     RowBox[{
      InterpretationBox[
       StyleBox[
        SubscriptBox[
         RowBox[{"\[LeftDoubleBracket]", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"i"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`i],
           Editable->False], ",", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"j"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`j],
           Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xTensor`Supercommutator[$CellContext`AP][
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma][$CellContext`j]],
       Editable->False], "\[Equal]", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False]}]}]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[29]//TableForm=",ExpressionUUID->"078f7bf3-d5bf-43ee-b9d8-a36886465e72"]
}, Open  ]],

Cell["\<\
How to solve for a replacement rule for a particularly ordered product a\
\[Diamond]b in terms of b\[Diamond]a:\
\>", "Text",ExpressionUUID->"a69bf0d2-bf9a-49d6-ba90-b7b87fe09ceb"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"CommuteAlgebraRule", "[", "AlgStruct_", "]"}], "[", 
   RowBox[{
    RowBox[{"P_", "?", "ProductQ"}], "[", 
    RowBox[{
     RowBox[{
      RowBox[{"a_", "?", "xTensorQ"}], "[", "___", "]"}], ",", 
     RowBox[{
      RowBox[{"b_", "?", "xTensorQ"}], "[", "___", "]"}]}], "]"}], "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"structureEq", "=", 
      RowBox[{"ExpandCommutator", "@", 
       RowBox[{"AlgStruct", "[", 
        RowBox[{"a", ",", "b"}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", 
    RowBox[{"With", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"solveFor", "=", 
        RowBox[{"First", "@", 
         RowBox[{"Cases", "[", 
          RowBox[{"structureEq", ",", 
           RowBox[{"P", "[", 
            RowBox[{
             RowBox[{"a", "[", "___", "]"}], ",", 
             RowBox[{"b", "[", "___", "]"}]}], "]"}], ",", "All"}], "]"}]}]}],
        "}"}], ",", "\[IndentingNewLine]", 
      RowBox[{"IndexSolve", "[", 
       RowBox[{"structureEq", ",", "solveFor", ",", 
        RowBox[{"MetricOn", "\[Rule]", "All"}], ",", 
        RowBox[{"ContractMetrics", "\[Rule]", "True"}]}], "]"}]}], "]"}]}], 
   "]"}]}]], "Input",
 CellLabel->"In[30]:=",ExpressionUUID->"52aa89ba-ed83-4672-8b18-c84a3c1f131f"],

Cell["Examples:", \
"Text",ExpressionUUID->"afcc5063-44ff-4b0f-bcfb-d2dca1e9127a"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"CommuteAlgebraRule", "[", "AlgebraStructure", "]"}], "[", 
  RowBox[{"AP", "[", 
   RowBox[{
    RowBox[{"\[Gamma]", "[", "j", "]"}], ",", 
    RowBox[{"\[Gamma]", "[", "k", "]"}]}], "]"}], "]"}]], "Input",
 CellLabel->"In[31]:=",ExpressionUUID->"b2cd8f7c-029e-44cd-ab8a-be73bafc9c58"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"HoldPattern", "[", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {
                UnderscriptBox[
                 UnderscriptBox["i", "_"], "_"]},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         PatternTest[
          Pattern[$CellContext`i, 
           Blank[]], TangentM`pmQ]],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {
                UnderscriptBox[
                 UnderscriptBox["j", "_"], "_"]},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][
         PatternTest[
          Pattern[$CellContext`j, 
           Blank[]], TangentM`pmQ]],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][
       PatternTest[
        Pattern[$CellContext`i, 
         Blank[]], TangentM`pmQ]], 
      $CellContext`\[Gamma][
       PatternTest[
        Pattern[$CellContext`j, 
         Blank[]], TangentM`pmQ]]],
     Editable->False], "]"}], "\[RuleDelayed]", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", "}"}], ",", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        InterpretationBox[
         StyleBox[
          RowBox[{
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`AP[
          $CellContext`\[Gamma][$CellContext`j], 
          $CellContext`\[Gamma][$CellContext`i]],
         Editable->False], ")"}]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False]}]}]}], "]"}]}], "}"}]], "Output",
 CellLabel->
  "Out[31]=",ExpressionUUID->"51ca6989-5bcb-4337-a505-25331a3a5f87"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["5. How to sort an associative product into a canonical form", \
"Subsubsection",ExpressionUUID->"2644e2ed-24a7-4fc1-8c8e-a2a648b04cce"],

Cell[TextData[{
 "We\[CloseCurlyQuote]re going to take the list AlgebraElements as an order \
on the elements. That is, if ",
 Cell[BoxData[
  FormBox[
   RowBox[{"AlgebraElements", "=", 
    RowBox[{"{", 
     RowBox[{
      SubscriptBox["a", "1"], ",", 
      SubscriptBox["a", "2"], ",", 
      RowBox[{"...", " ", 
       SubscriptBox["a", "n"]}]}], "}"}]}], TraditionalForm]],ExpressionUUID->
  "c08a6cbf-2bdc-4dc9-a56d-d75dacba049f"],
 ", then a general product ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{
      SubscriptBox["a", 
       SubscriptBox["i", "1"]], "\[Diamond]", 
      SubscriptBox["a", 
       SubscriptBox["i", "2"]], "\[Diamond]"}], "..."}], "\[Diamond]", 
    SubscriptBox["a", 
     SubscriptBox["i", "k"]]}], TraditionalForm]],ExpressionUUID->
  "47e029ac-91eb-4560-a9ec-3724f36a8745"],
 "will get reordered so that the subscripts are in increasing order as \
determined by AlgebraElements. If two adjacent elements have the same tensor ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "i"], TraditionalForm]],ExpressionUUID->
  "0104caa2-19d5-45a7-8cbf-aed736679bf2"],
 ", then we determine the order based on a canonical order on the indices."
}], "Text",ExpressionUUID->"c2d030b0-c212-4182-ab45-637b6774aacd"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"DisorderedProductQ", "[", "_", "]"}], "[", 
   RowBox[{
    RowBox[{
     RowBox[{"a_", "?", "xTensorQ"}], "[", "ai___", "]"}], ",", 
    RowBox[{"a_", "[", "bi___", "]"}]}], "]"}], ":=", 
  RowBox[{"!", 
   RowBox[{"OrderedQ", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", "ai", "}"}], ",", 
      RowBox[{"{", "bi", "}"}]}], "}"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"DisorderedProductQ", "[", "AlgList_", "]"}], "[", 
   RowBox[{
    RowBox[{
     RowBox[{"a_", "?", "xTensorQ"}], "[", "___", "]"}], ",", 
    RowBox[{
     RowBox[{"b_", "?", "xTensorQ"}], "[", "___", "]"}]}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Position", "[", 
     RowBox[{"AlgList", ",", "a"}], "]"}], "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "1"}], "]"}], "]"}], ">", 
   RowBox[{
    RowBox[{"Position", "[", 
     RowBox[{"AlgList", ",", "b"}], "]"}], "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "1"}], "]"}], "]"}]}]}]}], "Input",
 CellLabel->"In[32]:=",ExpressionUUID->"e1c40409-c776-4778-b754-0390445f7a14"],

Cell["Examples:", \
"Text",ExpressionUUID->"a8ee795e-dc1e-49e9-b6f4-8971bb285a22"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"AP", "[", 
        RowBox[{
         RowBox[{"#1", "[", "i", "]"}], ",", 
         RowBox[{"#2", "[", "j", "]"}]}], "]"}], ",", 
       RowBox[{
        RowBox[{"DisorderedProductQ", "[", "AlgebraElements", "]"}], "[", 
        RowBox[{
         RowBox[{"#1", "[", "i", "]"}], ",", 
         RowBox[{"#2", "[", "j", "]"}]}], "]"}]}], "}"}], "&"}], ",", 
    "AlgebraElements", ",", "AlgebraElements"}], "]"}], "//", 
  "TableForm"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"AP", "[", 
        RowBox[{
         RowBox[{"#1", "[", "j", "]"}], ",", 
         RowBox[{"#2", "[", "i", "]"}]}], "]"}], ",", 
       RowBox[{
        RowBox[{"DisorderedProductQ", "[", "AlgebraElements", "]"}], "[", 
        RowBox[{
         RowBox[{"#1", "[", "j", "]"}], ",", 
         RowBox[{"#2", "[", "i", "]"}]}], "]"}]}], "}"}], "&"}], ",", 
    "AlgebraElements", ",", "AlgebraElements"}], "]"}], "//", 
  "TableForm"}]}], "Input",
 CellLabel->"In[34]:=",ExpressionUUID->"77d5c2b4-620c-4aee-a9f9-942beb81e8d8"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     TagBox[GridBox[{
        {
         InterpretationBox[
          StyleBox[
           RowBox[{
            InterpretationBox[
             StyleBox[GridBox[{
                {"\[Gamma]", 
                 StyleBox[GridBox[{
                    {"i"},
                    {" "}
                   },
                   GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                  FontSize->Rational[39, 4]]}
               },
               
               GridBoxAlignment->{
                "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {{Center}}, "RowsIndexed" -> {}},
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.27999999999999997`], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {
                   Offset[0.2], {
                    Offset[0.4]}, 
                   Offset[0.2]}, "RowsIndexed" -> {}}],
              ShowAutoStyles->False,
              AutoSpacing->False],
             $CellContext`\[Gamma][$CellContext`i],
             Editable->False], "\[Diamond]", 
            InterpretationBox[
             StyleBox[GridBox[{
                {"\[Gamma]", 
                 StyleBox[GridBox[{
                    {"j"},
                    {" "}
                   },
                   GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                  FontSize->Rational[39, 4]]}
               },
               
               GridBoxAlignment->{
                "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {{Center}}, "RowsIndexed" -> {}},
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.27999999999999997`], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {
                   Offset[0.2], {
                    Offset[0.4]}, 
                   Offset[0.2]}, "RowsIndexed" -> {}}],
              ShowAutoStyles->False,
              AutoSpacing->False],
             $CellContext`\[Gamma][$CellContext`j],
             Editable->False]}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AP[
           $CellContext`\[Gamma][$CellContext`i], 
           $CellContext`\[Gamma][$CellContext`j]],
          Editable->False]},
        {"False"}
       },
       GridBoxAlignment->{
        "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{
            Offset[0.2]}}, "RowsIndexed" -> {}}],
      Column]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[34]//TableForm=",ExpressionUUID->"ffad2c8f-4d84-4f8e-ad0c-\
61acc02c979f"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     TagBox[GridBox[{
        {
         InterpretationBox[
          StyleBox[
           RowBox[{
            InterpretationBox[
             StyleBox[GridBox[{
                {"\[Gamma]", 
                 StyleBox[GridBox[{
                    {"j"},
                    {" "}
                   },
                   GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                  FontSize->Rational[39, 4]]}
               },
               
               GridBoxAlignment->{
                "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {{Center}}, "RowsIndexed" -> {}},
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.27999999999999997`], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {
                   Offset[0.2], {
                    Offset[0.4]}, 
                   Offset[0.2]}, "RowsIndexed" -> {}}],
              ShowAutoStyles->False,
              AutoSpacing->False],
             $CellContext`\[Gamma][$CellContext`j],
             Editable->False], "\[Diamond]", 
            InterpretationBox[
             StyleBox[GridBox[{
                {"\[Gamma]", 
                 StyleBox[GridBox[{
                    {"i"},
                    {" "}
                   },
                   GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                  FontSize->Rational[39, 4]]}
               },
               
               GridBoxAlignment->{
                "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {{Center}}, "RowsIndexed" -> {}},
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.27999999999999997`], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                 "Rows" -> {
                   Offset[0.2], {
                    Offset[0.4]}, 
                   Offset[0.2]}, "RowsIndexed" -> {}}],
              ShowAutoStyles->False,
              AutoSpacing->False],
             $CellContext`\[Gamma][$CellContext`i],
             Editable->False]}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AP[
           $CellContext`\[Gamma][$CellContext`j], 
           $CellContext`\[Gamma][$CellContext`i]],
          Editable->False]},
        {"True"}
       },
       GridBoxAlignment->{
        "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.5599999999999999]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{
            Offset[0.2]}}, "RowsIndexed" -> {}}],
      Column]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[35]//TableForm=",ExpressionUUID->"3074cd8a-922e-470a-9700-8d123432f13e"]
}, Open  ]],

Cell["\<\
How to actually do the sorting. Find disordered products, apply \
(anti-)commutation relations, keep going until stable.\
\>", "Text",ExpressionUUID->"3e1ad0ce-e588-4ee3-b9de-95c58f19830f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"SortAlgebraProduct", "[", 
    RowBox[{
     RowBox[{"P_", "?", "ProductQ"}], ",", "AlgList_", ",", "AlgStruct_"}], 
    "]"}], "[", "expr_", "]"}], ":=", 
  RowBox[{"expr", "//.", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"HoldPattern", "[", 
       RowBox[{"P", "[", 
        RowBox[{"left___", ",", "a_", ",", "b_", ",", "right___"}], "]"}], 
       "]"}], "/;", 
      RowBox[{
       RowBox[{"DisorderedProductQ", "[", "AlgList", "]"}], "[", 
       RowBox[{"a", ",", "b"}], "]"}]}], "\[RuleDelayed]", 
     RowBox[{"With", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"newInner", "=", 
         RowBox[{
          RowBox[{"P", "[", 
           RowBox[{"a", ",", "b"}], "]"}], "/.", 
          RowBox[{
           RowBox[{"CommuteAlgebraRule", "[", "AlgStruct", "]"}], "[", 
           RowBox[{"P", "[", 
            RowBox[{"a", ",", "b"}], "]"}], "]"}]}]}], "}"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"P", "[", 
        RowBox[{"left", ",", "newInner", ",", "right"}], "]"}]}], "]"}]}], 
    "}"}]}]}]], "Input",
 CellLabel->
  "In[36]:=",ExpressionUUID->"4ba2dc55-6e91-4722-a0f4-62a4372dddac"]
}, Closed]],

Cell[CellGroupData[{

Cell["6. Example of sorting", \
"Subsubsection",ExpressionUUID->"b566e436-6b06-4259-9443-822857f6b32c"],

Cell[BoxData[
 RowBox[{
  RowBox[{"mySAP", ":=", 
   RowBox[{"SortAlgebraProduct", "[", 
    RowBox[{"AP", ",", "AlgebraElements", ",", "AlgebraStructure"}], "]"}]}], 
  ";"}]], "Input",
 CellLabel->"In[37]:=",ExpressionUUID->"fff0bbde-2883-4ca8-9070-d476fda46180"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Pairs", "=", 
   RowBox[{"Flatten", "@", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "i", "]"}], ",", 
           RowBox[{"#2", "[", "j", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements"}], "]"}], ",", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "j", "]"}], ",", 
           RowBox[{"#2", "[", "i", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements"}], "]"}]}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Transpose", "@", 
    RowBox[{"{", 
     RowBox[{"Pairs", ",", 
      RowBox[{"mySAP", "@", "Pairs"}]}], "}"}]}], "//", 
   "ScreenDollarIndices"}], "//", "TableForm"}]}], "Input",
 CellLabel->"In[38]:=",ExpressionUUID->"d334779e-c542-4b69-a6a4-0a996852edec"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`j]],
      Editable->False], 
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`j]],
      Editable->False]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`i]],
      Editable->False], 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        InterpretationBox[
         StyleBox[
          RowBox[{
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`AP[
          $CellContext`\[Gamma][$CellContext`i], 
          $CellContext`\[Gamma][$CellContext`j]],
         Editable->False], ")"}]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"j", "i"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`j, $CellContext`i],
        Editable->False]}]}]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[39]//TableForm=",ExpressionUUID->"8995d0ec-625c-4908-9f10-17dbefb13b9e"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetOptions", "[", 
   RowBox[{"ToCanonical", ",", 
    RowBox[{"UseMetricOnVBundle", "\[Rule]", "None"}]}], "]"}], 
  ";"}]], "Input",
 CellLabel->"In[40]:=",ExpressionUUID->"6df4e132-0c3a-447a-a236-faa5bd742b5b"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Trips", "=", 
   RowBox[{"Flatten", "@", 
    RowBox[{"{", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "i", "]"}], ",", 
           RowBox[{"#2", "[", "j", "]"}], ",", 
           RowBox[{"#3", "[", "k", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "i", "]"}], ",", 
           RowBox[{"#2", "[", "k", "]"}], ",", 
           RowBox[{"#3", "[", "j", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "j", "]"}], ",", 
           RowBox[{"#2", "[", "i", "]"}], ",", 
           RowBox[{"#3", "[", "k", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "j", "]"}], ",", 
           RowBox[{"#2", "[", "k", "]"}], ",", 
           RowBox[{"#3", "[", "i", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "k", "]"}], ",", 
           RowBox[{"#2", "[", "i", "]"}], ",", 
           RowBox[{"#3", "[", "j", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Outer", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"AP", "[", 
          RowBox[{
           RowBox[{"#1", "[", "k", "]"}], ",", 
           RowBox[{"#2", "[", "j", "]"}], ",", 
           RowBox[{"#3", "[", "i", "]"}]}], "]"}], "&"}], ",", 
        "AlgebraElements", ",", "AlgebraElements", ",", "AlgebraElements"}], 
       "]"}]}], "\[IndentingNewLine]", "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Transpose", "@", 
   RowBox[{"{", 
    RowBox[{"Trips", ",", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"Trips", "//", "mySAP"}], "//", "ContractMetric"}], "//", 
       "ToCanonical"}], "//", "ScreenDollarIndices"}]}], "}"}]}], "//", 
  "TableForm"}]}], "Input",
 CellLabel->"In[41]:=",ExpressionUUID->"7eebbaf2-069a-4f10-9872-4ac519643882"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`k]],
      Editable->False], 
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`k]],
      Editable->False]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`k], 
       $CellContext`\[Gamma][$CellContext`j]],
      Editable->False], 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        InterpretationBox[
         StyleBox[
          RowBox[{
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"k"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`k],
            Editable->False]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`AP[
          $CellContext`\[Gamma][$CellContext`i], 
          $CellContext`\[Gamma][$CellContext`j], 
          $CellContext`\[Gamma][$CellContext`k]],
         Editable->False], ")"}]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"j", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`j, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}]}]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`k]],
      Editable->False], 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        InterpretationBox[
         StyleBox[
          RowBox[{
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"k"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`k],
            Editable->False]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`AP[
          $CellContext`\[Gamma][$CellContext`i], 
          $CellContext`\[Gamma][$CellContext`j], 
          $CellContext`\[Gamma][$CellContext`k]],
         Editable->False], ")"}]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"k"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`k],
        Editable->False]}]}]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`k], 
       $CellContext`\[Gamma][$CellContext`i]],
      Editable->False], 
     RowBox[{
      InterpretationBox[
       StyleBox[
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"i"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`i],
          Editable->False], "\[Diamond]", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"j"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`j],
          Editable->False], "\[Diamond]", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"k"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`k],
          Editable->False]}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AP[
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma][$CellContext`j], 
        $CellContext`\[Gamma][$CellContext`k]],
       Editable->False], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}], "-", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"k"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`k],
        Editable->False]}]}]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`k], 
       $CellContext`\[Gamma][$CellContext`i], 
       $CellContext`\[Gamma][$CellContext`j]],
      Editable->False], 
     RowBox[{
      InterpretationBox[
       StyleBox[
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"i"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`i],
          Editable->False], "\[Diamond]", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"j"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`j],
          Editable->False], "\[Diamond]", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Gamma]", 
              StyleBox[GridBox[{
                 {"k"},
                 {" "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->Rational[39, 4]]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`\[Gamma][$CellContext`k],
          Editable->False]}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AP[
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma][$CellContext`j], 
        $CellContext`\[Gamma][$CellContext`k]],
       Editable->False], "-", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"j", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`j, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}]}]},
    {
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"k"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`k],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"j"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`j],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {"i"},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][$CellContext`i],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][$CellContext`k], 
       $CellContext`\[Gamma][$CellContext`j], 
       $CellContext`\[Gamma][$CellContext`i]],
      Editable->False], 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        InterpretationBox[
         StyleBox[
          RowBox[{
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"i"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`i],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"j"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`j],
            Editable->False], "\[Diamond]", 
           InterpretationBox[
            StyleBox[GridBox[{
               {"\[Gamma]", 
                StyleBox[GridBox[{
                   {"k"},
                   {" "}
                  },
                  GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                 FontSize->Rational[39, 4]]}
              },
              
              GridBoxAlignment->{
               "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
                "Rows" -> {{Center}}, "RowsIndexed" -> {}},
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.27999999999999997`], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
                "Rows" -> {
                  Offset[0.2], {
                   Offset[0.4]}, 
                  Offset[0.2]}, "RowsIndexed" -> {}}],
             ShowAutoStyles->False,
             AutoSpacing->False],
            $CellContext`\[Gamma][$CellContext`k],
            Editable->False]}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`AP[
          $CellContext`\[Gamma][$CellContext`i], 
          $CellContext`\[Gamma][$CellContext`j], 
          $CellContext`\[Gamma][$CellContext`k]],
         Editable->False], ")"}]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"j", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`j, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"i"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`i],
        Editable->False]}], "-", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "k"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`k],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"j"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`j],
        Editable->False]}], "+", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"k"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`k],
        Editable->False]}]}]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[42]//TableForm=",ExpressionUUID->"4a929f0d-d2bb-4dd4-a3bf-a595d8b26cdc"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["7. Some simple Dirac algebra identities", \
"Subsubsection",ExpressionUUID->"92754e4b-9fd3-429e-a752-62a4b48a9f77"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Commutator", "[", "AP", "]"}], "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", "ExpandCommutator"}], "//", 
  "mySAP"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Anticommutator", "[", "AP", "]"}], "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", "ExpandCommutator"}], "//", "mySAP"}]}], "Input",
 CellLabel->"In[43]:=",ExpressionUUID->"d85f2287-8e15-47e7-a47e-456e401e90ae"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   SubscriptBox[
    RowBox[{"[", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "]"}], "\[Diamond]"],
   ShowAutoStyles->False,
   AutoSpacing->False],
  xAct`xTensor`Commutator[$CellContext`AP][
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b]],
  Editable->False]], "Output",
 CellLabel->"Out[43]=",ExpressionUUID->"ad96880b-f3a5-43e1-8b8a-6ee1e4d58831"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"b"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`b],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`b]],
    Editable->False]}], "-", 
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "a"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`a],
    Editable->False]}]}]], "Output",
 CellLabel->"Out[44]=",ExpressionUUID->"02b35415-8802-4b8c-b7c8-47b283f1ca30"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   SubscriptBox[
    RowBox[{"{", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "}"}], "\[Diamond]"],
   ShowAutoStyles->False,
   AutoSpacing->False],
  xAct`xTensor`Anticommutator[$CellContext`AP][
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b]],
  Editable->False]], "Output",
 CellLabel->"Out[45]=",ExpressionUUID->"5dd09055-4eca-4923-89f5-ad46ff264cf3"],

Cell[BoxData[
 RowBox[{"2", " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"g", 
       StyleBox[GridBox[{
          {"b", "a"},
          {" ", " "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`g[$CellContext`b, $CellContext`a],
   Editable->False]}]], "Output",
 CellLabel->
  "Out[46]=",ExpressionUUID->"e9305838-9727-4568-b557-a1f6b30faaf4"]
}, Open  ]],

Cell["Contraction on product of two \[Gamma]\[CloseCurlyQuote]s identity. \
Save this rule.", \
"Text",ExpressionUUID->"8a6e2524-fef0-4c40-b6e9-077a269a71c7"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", 
    RowBox[{"-", "a"}], "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"SeparateMetric", "[", "]"}], "@", "%"}], "\[IndentingNewLine]", 
 RowBox[{"MapAt", "[", 
  RowBox[{"Symmetrize", ",", "%", ",", "1"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}], "\[IndentingNewLine]", 
 RowBox[{"\[Gamma]\[Gamma]ContractRule", "=", 
  RowBox[{"MakeRule", "[", 
   RowBox[{
    RowBox[{"Evaluate", "@", 
     RowBox[{"{", 
      RowBox[{"%%%%", ",", "%"}], "}"}]}], ",", 
    RowBox[{"MetricOn", "\[Rule]", "All"}]}], "]"}]}]}], "Input",
 CellLabel->"In[47]:=",ExpressionUUID->"0cae49b2-e210-497a-b57e-73c55dc5da38"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {" "},
            {"a"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][-$CellContext`a],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][-$CellContext`a]],
  Editable->False]], "Output",
 CellLabel->"Out[47]=",ExpressionUUID->"afc77874-97f5-484d-b09c-7ff03f1cad9b"],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`b]],
   Editable->False], " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"g", 
       StyleBox[GridBox[{
          {" ", " "},
          {"b", "a"}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`g[-$CellContext`b, -$CellContext`a],
   Editable->False]}]], "Output",
 CellLabel->"Out[48]=",ExpressionUUID->"6ac64d06-0fa6-4ae4-beb8-7059d45104e7"],

Cell[BoxData[
 RowBox[{
  FractionBox["1", "2"], " ", 
  RowBox[{"(", 
   RowBox[{
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"a"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`a],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"b"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`b],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`a], 
      $CellContext`\[Gamma][$CellContext`b]],
     Editable->False], "+", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"b"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`b],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Gamma]", 
            StyleBox[GridBox[{
               {"a"},
               {" "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma][$CellContext`a],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma][$CellContext`b], 
      $CellContext`\[Gamma][$CellContext`a]],
     Editable->False]}], ")"}], " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"g", 
       StyleBox[GridBox[{
          {" ", " "},
          {"b", "a"}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`g[-$CellContext`b, -$CellContext`a],
   Editable->False]}]], "Output",
 CellLabel->"Out[49]=",ExpressionUUID->"0cfd6e6a-c9fb-44a7-b4cf-91a42e4268bf"],

Cell[BoxData["4"], "Output",
 CellLabel->"Out[50]=",ExpressionUUID->"45dc6031-29c6-469b-bae7-01414178cdc7"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    RowBox[{"HoldPattern", "[", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {
                 UnderscriptBox[
                  UnderscriptBox["a", "_"], "_"]},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][
          PatternTest[
           Pattern[$CellContext`a, 
            Blank[Symbol]], TangentM`Q]],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {" "},
                {
                 UnderscriptBox[
                  UnderscriptBox["a", "_"], "_"]}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][-PatternTest[
            Pattern[$CellContext`a, 
             Blank[Symbol]], TangentM`Q]],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][
        PatternTest[
         Pattern[$CellContext`a, 
          Blank[Symbol]], TangentM`Q]], 
       $CellContext`\[Gamma][-PatternTest[
          Pattern[$CellContext`a, 
           Blank[Symbol]], TangentM`Q]]],
      Editable->False], "]"}], "\[RuleDelayed]", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", "}"}], ",", "4"}], "]"}]}], ",", 
   RowBox[{
    RowBox[{"HoldPattern", "[", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {" "},
                {
                 UnderscriptBox[
                  UnderscriptBox["a", "_"], "_"]}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][-PatternTest[
            Pattern[$CellContext`a, 
             Blank[Symbol]], TangentM`Q]],
         Editable->False], "\[Diamond]", 
        InterpretationBox[
         StyleBox[GridBox[{
            {"\[Gamma]", 
             StyleBox[GridBox[{
                {
                 UnderscriptBox[
                  UnderscriptBox["a", "_"], "_"]},
                {" "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->Rational[39, 4]]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          ShowAutoStyles->False,
          AutoSpacing->False],
         $CellContext`\[Gamma][
          PatternTest[
           Pattern[$CellContext`a, 
            Blank[Symbol]], TangentM`Q]],
         Editable->False]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AP[
       $CellContext`\[Gamma][-PatternTest[
          Pattern[$CellContext`a, 
           Blank[Symbol]], TangentM`Q]], 
       $CellContext`\[Gamma][
        PatternTest[
         Pattern[$CellContext`a, 
          Blank[Symbol]], TangentM`Q]]],
      Editable->False], "]"}], "\[RuleDelayed]", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", "}"}], ",", "4"}], "]"}]}]}], "}"}]], "Output",
 CellLabel->
  "Out[51]=",ExpressionUUID->"8ac98b35-cd56-45f5-aca6-bcaee477212c"]
}, Open  ]],

Cell["Contraction on product of three \[Gamma]\[CloseCurlyQuote]s:", \
"Text",ExpressionUUID->"56b35287-9917-4e14-8b77-eee90df78d42"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", 
    RowBox[{"-", "a"}], "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}], "\[IndentingNewLine]", 
 RowBox[{"%", "/.", "\[Gamma]\[Gamma]ContractRule"}]}], "Input",
 CellLabel->"In[52]:=",ExpressionUUID->"3bc2e9a6-8342-4a8d-957a-7f9b48c5dc51"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {" "},
            {"a"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][-$CellContext`a],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b], 
   $CellContext`\[Gamma][-$CellContext`a]],
  Editable->False]], "Output",
 CellLabel->"Out[52]=",ExpressionUUID->"5d0c88b2-fef7-4a5f-b8f8-2c0c1a7cea2d"],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {" "},
             {"a"}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][-$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][-$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`b]],
   Editable->False], "-", 
  RowBox[{"6", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"b"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`b],
    Editable->False]}]}]], "Output",
 CellLabel->"Out[53]=",ExpressionUUID->"6250b130-1a21-4762-a4ac-d25e32996d26"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "2"}], " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"\[Gamma]", 
       StyleBox[GridBox[{
          {"b"},
          {" "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`\[Gamma][$CellContext`b],
   Editable->False]}]], "Output",
 CellLabel->
  "Out[54]=",ExpressionUUID->"17395875-1568-402e-b79c-ad7fa548527b"]
}, Open  ]],

Cell["Contraction on product of four \[Gamma]\[CloseCurlyQuote]s:", \
"Text",ExpressionUUID->"f5107ef2-aad4-4371-82b2-af339be5fad1"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "c", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", 
    RowBox[{"-", "a"}], "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", "mySAP"}], "//", "ToCanonical"}], "\[IndentingNewLine]", 

 RowBox[{"%", "/.", "\[Gamma]\[Gamma]ContractRule"}]}], "Input",
 CellLabel->"In[55]:=",ExpressionUUID->"78621f21-ba87-4f4e-a432-8f4fa9639db6"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"c"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`c],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {" "},
            {"a"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][-$CellContext`a],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b], 
   $CellContext`\[Gamma][$CellContext`c], 
   $CellContext`\[Gamma][-$CellContext`a]],
  Editable->False]], "Output",
 CellLabel->"Out[55]=",ExpressionUUID->"df12b952-efe9-47bf-8367-403c71ae0ce1"],

Cell[BoxData[
 RowBox[{
  RowBox[{"4", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"b"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`b],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"c"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`c],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`b], 
     $CellContext`\[Gamma][$CellContext`c]],
    Editable->False]}], "-", 
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {" "},
             {"a"}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][-$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"c"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`c],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][-$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`b], 
    $CellContext`\[Gamma][$CellContext`c]],
   Editable->False], "+", 
  RowBox[{"4", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "c"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`c],
    Editable->False]}]}]], "Output",
 CellLabel->"Out[56]=",ExpressionUUID->"f5087001-1087-46f7-b3a0-a6eaf1c758b2"],

Cell[BoxData[
 RowBox[{"4", " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"g", 
       StyleBox[GridBox[{
          {"b", "c"},
          {" ", " "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`g[$CellContext`b, $CellContext`c],
   Editable->False]}]], "Output",
 CellLabel->
  "Out[57]=",ExpressionUUID->"b51f9a0d-9a43-43cd-a21c-4f10a749b2b4"]
}, Open  ]],

Cell["Contraction on product of five \[Gamma]\[CloseCurlyQuote]s:", \
"Text",ExpressionUUID->"27b798ac-f500-4790-af10-daf30be573de"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "d", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "c", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", 
    RowBox[{"-", "a"}], "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", "mySAP"}], "//", 
  "ToCanonical"}], "\[IndentingNewLine]", 
 RowBox[{"%", "/.", "\[Gamma]\[Gamma]ContractRule"}]}], "Input",
 CellLabel->"In[58]:=",ExpressionUUID->"44bd8660-49a5-46f9-9dc5-f03a77f636e7"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"d"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`d],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"c"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`c],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {" "},
            {"a"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][-$CellContext`a],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`d], 
   $CellContext`\[Gamma][$CellContext`c], 
   $CellContext`\[Gamma][$CellContext`b], 
   $CellContext`\[Gamma][-$CellContext`a]],
  Editable->False]], "Output",
 CellLabel->"Out[58]=",ExpressionUUID->"19422d3a-8e6e-4aa9-b2f2-82d85aec1ea7"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"b"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`b],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"c"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`c],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"d"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`d],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`b], 
     $CellContext`\[Gamma][$CellContext`c], 
     $CellContext`\[Gamma][$CellContext`d]],
    Editable->False]}], "-", 
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {" "},
             {"a"}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][-$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"c"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`c],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"d"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`d],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][-$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`b], 
    $CellContext`\[Gamma][$CellContext`c], 
    $CellContext`\[Gamma][$CellContext`d]],
   Editable->False], "+", 
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {" "},
              {"a"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][-$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"d"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`d],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][-$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`d]],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "c"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`c],
    Editable->False]}], "-", 
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {" "},
              {"a"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][-$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"c"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`c],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][-$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`c]],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`d],
    Editable->False]}], "+", 
  RowBox[{"2", " ", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {" "},
              {"a"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][-$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"b"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`b],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][-$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`b]],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"c", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`c, $CellContext`d],
    Editable->False]}], "-", 
  RowBox[{"8", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"c", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`c, $CellContext`d],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"b"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`b],
    Editable->False]}], "+", 
  RowBox[{"8", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`d],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"c"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`c],
    Editable->False]}], "-", 
  RowBox[{"8", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "c"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`c],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"d"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`d],
    Editable->False]}]}]], "Output",
 CellLabel->"Out[59]=",ExpressionUUID->"5a177686-8364-4dd0-b8d6-c842fc961d31"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "2"}], " ", 
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"c"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`c],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"d"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`d],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][$CellContext`b], 
    $CellContext`\[Gamma][$CellContext`c], 
    $CellContext`\[Gamma][$CellContext`d]],
   Editable->False]}]], "Output",
 CellLabel->
  "Out[60]=",ExpressionUUID->"0762b9a1-a28b-41dc-8c60-a4482dcfc34d"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
 "8. The ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["\[Gamma]", "5"], TraditionalForm]],ExpressionUUID->
  "63be82ea-9567-4110-a8fc-827a5210283f"],
 " algebra element"
}], "Subsubsection",ExpressionUUID->"cc97d62f-65d0-451c-8d45-4f6dd9a9911b"],

Cell[TextData[{
 "First, an explicit expression, ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SuperscriptBox["\[Gamma]", "5"], "=", 
    RowBox[{
     FractionBox["\[ImaginaryI]", 
      RowBox[{"4", "!"}]], 
     SubscriptBox["\[Epsilon]", "abcd"], 
     SuperscriptBox["\[Gamma]", "a"], 
     SuperscriptBox["\[Gamma]", "b"], 
     SuperscriptBox["\[Gamma]", "c"], 
     SuperscriptBox["\[Gamma]", "d"]}]}], TraditionalForm]],ExpressionUUID->
  "e51aef3f-a1fa-4a5c-80e9-517b5a62af20"]
}], "Text",ExpressionUUID->"2fb1f47a-4300-4a32-8b27-e10d968d8819"],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]5Explicit", "[", "]"}], ":=", 
  RowBox[{"Module", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "}"}], ",", 
    RowBox[{
     FractionBox["\[ImaginaryI]", 
      RowBox[{"4", "!"}]], 
     RowBox[{"epsilong", "[", 
      RowBox[{
       RowBox[{"-", "a"}], ",", 
       RowBox[{"-", "b"}], ",", 
       RowBox[{"-", "c"}], ",", 
       RowBox[{"-", "d"}]}], "]"}], 
     RowBox[{"AP", "[", 
      RowBox[{
       RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
       RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
       RowBox[{"\[Gamma]", "[", "c", "]"}], ",", 
       RowBox[{"\[Gamma]", "[", "d", "]"}]}], "]"}]}]}], "]"}]}]], "Input",
 CellLabel->"In[61]:=",ExpressionUUID->"f6c4ebf8-effb-4f5c-b466-757f34873750"],

Cell[TextData[{
 "Explicitly show that ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      SuperscriptBox["\[Gamma]", "5"], ")"}], "2"], "=", "id"}], 
   TraditionalForm]],ExpressionUUID->"0433981a-faf9-4dc4-8b8b-9126ab602757"],
 ". Takes about 1 minute on my computer."
}], "Text",ExpressionUUID->"1b1d0196-bb8a-43d3-aac4-bbdcbc8662a6"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"AP", "[", 
      RowBox[{
       RowBox[{"\[Gamma]5Explicit", "[", "]"}], ",", 
       RowBox[{"\[Gamma]5Explicit", "[", "]"}]}], "]"}], "//", 
     "ContractMetric"}], ")"}], "//.", "\[Gamma]\[Gamma]ContractRule"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"%", "//", "mySAP"}], "//", "ContractMetric"}], ")"}], "//.", 
      "\[Gamma]\[Gamma]ContractRule"}], "//", "mySAP"}], "//", 
    "ContractMetric"}], ")"}], "//.", 
  "\[Gamma]\[Gamma]ContractRule"}]}], "Input",
 CellLabel->"In[62]:=",ExpressionUUID->"31c32ea3-619c-4cc5-aaf9-94de91534e80"],

Cell[BoxData["1"], "Output",
 CellLabel->
  "Out[63]=",ExpressionUUID->"bacd2d1f-146b-460c-a873-856534df35cf"]
}, Open  ]],

Cell[TextData[{
 "Prove that ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "5"]}], 
     SuperscriptBox["\[Gamma]", "d"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"]}], "=", 
    RowBox[{
     RowBox[{
      SuperscriptBox["\[Gamma]", "a"], 
      SuperscriptBox["\[Gamma]", "b"], 
      SuperscriptBox["\[Gamma]", "c"]}], "-", 
     RowBox[{
      SuperscriptBox["g", "ab"], 
      SuperscriptBox["\[Gamma]", "c"]}], "-", 
     RowBox[{
      SuperscriptBox["g", "bc"], 
      SuperscriptBox["\[Gamma]", "a"]}], "+", 
     RowBox[{
      SuperscriptBox["g", "ac"], 
      SuperscriptBox["\[Gamma]", "b"]}]}]}], TraditionalForm]],
  ExpressionUUID->"48ff8afb-66fd-4aff-993f-4f28b937211c"],
 "."
}], "Text",ExpressionUUID->"43c7c554-72c9-402b-a2b8-f33bd77b6ee8"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], " ", 
    RowBox[{"AP", "[", 
     RowBox[{
      RowBox[{"\[Gamma]5Explicit", "[", "]"}], ",", 
      RowBox[{"\[Gamma]", "[", "d", "]"}]}], "]"}], 
    RowBox[{"epsilong", "[", 
     RowBox[{
      RowBox[{"-", "d"}], ",", "a", ",", "b", ",", "c"}], "]"}]}], "\[Equal]", 
   RowBox[{
    RowBox[{"AP", "[", 
     RowBox[{
      RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
      RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
      RowBox[{"\[Gamma]", "[", "c", "]"}]}], "]"}], "-", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"a", ",", "b"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "c", "]"}]}], "-", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"b", ",", "c"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "a", "]"}]}], "+", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"a", ",", "c"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "b", "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"%", "//", "ContractMetric"}], "//", "mySAP"}], "//", 
      "ContractMetric"}], ")"}], "//.", "\[Gamma]\[Gamma]ContractRule"}], "//",
    "mySAP"}], "//", "ToCanonical"}]}], "Input",
 CellLabel->"In[64]:=",ExpressionUUID->"5a6979c9-b7ea-43af-8b8d-67b7d4598adf"],

Cell[BoxData["True"], "Output",
 CellLabel->
  "Out[65]=",ExpressionUUID->"9ea4a3be-be61-47ef-985c-20cce4ccc9a9"]
}, Open  ]],

Cell[TextData[{
 "Starting from this proof, hit both sides with ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox[
    SubscriptBox["\[Epsilon]", "abc"], "e"], TraditionalForm]],
  ExpressionUUID->"060e65b4-89b6-40c0-b4c1-354c1223f294"],
 ", and use the fact that ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}], "=", 
    RowBox[{
     RowBox[{"3", "!"}], 
     SubsuperscriptBox["\[Delta]", "d", "e"]}]}], TraditionalForm]],
  ExpressionUUID->"cd5a0105-85aa-4215-81d4-ff80bdede493"],
 ":\n  ",
 Cell[BoxData[{
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "5"]}], 
     SuperscriptBox["\[Gamma]", "d"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"]}], "=", 
    RowBox[{
     RowBox[{
      SuperscriptBox["\[Gamma]", "a"], 
      SuperscriptBox["\[Gamma]", "b"], 
      SuperscriptBox["\[Gamma]", "c"]}], "-", 
     RowBox[{
      SuperscriptBox["g", "ab"], 
      SuperscriptBox["\[Gamma]", "c"]}], "-", 
     RowBox[{
      SuperscriptBox["g", "bc"], 
      SuperscriptBox["\[Gamma]", "a"]}], "+", 
     RowBox[{
      SuperscriptBox["g", "ac"], 
      SuperscriptBox["\[Gamma]", "b"]}]}]}], 
   TraditionalForm], "\[IndentingNewLine]", 
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "5"]}], 
     SuperscriptBox["\[Gamma]", "d"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}], "=", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        SuperscriptBox["\[Gamma]", "a"], 
        SuperscriptBox["\[Gamma]", "b"], 
        SuperscriptBox["\[Gamma]", "c"]}], "-", 
       RowBox[{
        SuperscriptBox["g", "ab"], 
        SuperscriptBox["\[Gamma]", "c"]}], "-", 
       RowBox[{
        SuperscriptBox["g", "bc"], 
        SuperscriptBox["\[Gamma]", "a"]}], "+", 
       RowBox[{
        SuperscriptBox["g", "ac"], 
        SuperscriptBox["\[Gamma]", "b"]}]}], ")"}], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}]}], 
   TraditionalForm], "\[IndentingNewLine]", 
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "5"]}], 
     SuperscriptBox["\[Gamma]", "e"]}], "=", 
    RowBox[{
     FractionBox["1", 
      RowBox[{"3", "!"}]], 
     SuperscriptBox["\[Gamma]", "a"], 
     SuperscriptBox["\[Gamma]", "b"], 
     SuperscriptBox["\[Gamma]", "c"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"], "         ", 
     RowBox[{"(", "\[Star]", ")"}]}]}], TraditionalForm]}],ExpressionUUID->
  "ebd66b7e-b2c1-4e15-a120-21b50d7be7e0"]
}], "Text",ExpressionUUID->"c814e242-0305-4735-9cfc-c44e4d4bc50c"],

Cell[TextData[{
 "But now change the order to ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"-", 
     SuperscriptBox["\[ImaginaryI]\[Gamma]", "d"]}], 
    SuperscriptBox["\[Gamma]", "5"], 
    SuperscriptBox[
     SubscriptBox["\[Epsilon]", "d"], "abc"]}], TraditionalForm]],
  ExpressionUUID->"317c85e6-044a-4add-8998-ac771160dd99"],
 ", and you can prove that\n  ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "d"]}], 
     SuperscriptBox["\[Gamma]", "5"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"]}], "=", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["\[Gamma]", "a"]}], 
      SuperscriptBox["\[Gamma]", "b"], 
      SuperscriptBox["\[Gamma]", "c"]}], "+", 
     RowBox[{
      SuperscriptBox["g", "ab"], 
      SuperscriptBox["\[Gamma]", "c"]}], "+", 
     RowBox[{
      SuperscriptBox["g", "bc"], 
      SuperscriptBox["\[Gamma]", "a"]}], "-", 
     RowBox[{
      SuperscriptBox["g", "ac"], 
      RowBox[{
       SuperscriptBox["\[Gamma]", "b"], ":"}]}]}]}], TraditionalForm]],
  ExpressionUUID->"6f926ef0-cdda-4b00-9ab1-b238eef9ff50"]
}], "Text",ExpressionUUID->"89f20bbc-e9d6-4c1f-99fa-03bffdab1bbc"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], " ", 
    RowBox[{"AP", "[", 
     RowBox[{
      RowBox[{"\[Gamma]", "[", "d", "]"}], ",", 
      RowBox[{"\[Gamma]5Explicit", "[", "]"}]}], "]"}], 
    RowBox[{"epsilong", "[", 
     RowBox[{
      RowBox[{"-", "d"}], ",", "a", ",", "b", ",", "c"}], "]"}]}], "\[Equal]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{"AP", "[", 
      RowBox[{
       RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
       RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
       RowBox[{"\[Gamma]", "[", "c", "]"}]}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"a", ",", "b"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "c", "]"}]}], "+", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"b", ",", "c"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "a", "]"}]}], "-", 
    RowBox[{
     RowBox[{"g", "[", 
      RowBox[{"a", ",", "c"}], "]"}], 
     RowBox[{"\[Gamma]", "[", "b", "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"%", "//", "ContractMetric"}], "//", "mySAP"}], "//", 
      "ContractMetric"}], ")"}], "//.", "\[Gamma]\[Gamma]ContractRule"}], "//",
    "mySAP"}], "//", "ToCanonical"}]}], "Input",
 CellLabel->"In[66]:=",ExpressionUUID->"90dd0020-818e-46c5-8e8b-d95fd86f95e5"],

Cell[BoxData["True"], "Output",
 CellLabel->
  "Out[67]=",ExpressionUUID->"907d9c63-39c2-47de-b668-3b2cb53097ed"]
}, Open  ]],

Cell[TextData[{
 "But now in the same way as (\[Star]), we can find another way of expressing \
",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox["1", 
     RowBox[{"3", "!"}]], 
    SuperscriptBox["\[Gamma]", "a"], 
    SuperscriptBox["\[Gamma]", "b"], 
    SuperscriptBox["\[Gamma]", "c"], 
    SuperscriptBox[
     SubscriptBox["\[Epsilon]", "abc"], "e"]}], TraditionalForm]],
  ExpressionUUID->"86715e47-24a2-469f-9b4d-6586be14fe05"],
 ":\n  ",
 Cell[BoxData[{
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox["\[ImaginaryI]\[Gamma]", "d"]}], 
     SuperscriptBox["\[Gamma]", "5"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "d"], "abc"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}], "=", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         SuperscriptBox["\[Gamma]", "a"]}], 
        SuperscriptBox["\[Gamma]", "b"], 
        SuperscriptBox["\[Gamma]", "c"]}], "+", 
       RowBox[{
        SuperscriptBox["g", "ab"], 
        SuperscriptBox["\[Gamma]", "c"]}], "+", 
       RowBox[{
        SuperscriptBox["g", "bc"], 
        SuperscriptBox["\[Gamma]", "a"]}], "-", 
       RowBox[{
        SuperscriptBox["g", "ac"], 
        SuperscriptBox["\[Gamma]", "b"]}]}], ")"}], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}]}], 
   TraditionalForm], "\[IndentingNewLine]", 
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], " ", 
     SuperscriptBox["\[Gamma]", "e"], 
     SuperscriptBox["\[Gamma]", "5"]}], "=", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", 
       RowBox[{"3", "!"}]]}], 
     SuperscriptBox["\[Gamma]", "a"], 
     SuperscriptBox["\[Gamma]", "b"], 
     SuperscriptBox["\[Gamma]", "c"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"], "         ", 
     RowBox[{"(", 
      RowBox[{"\[Star]", "\[Star]"}], ")"}]}]}], TraditionalForm]}],
  ExpressionUUID->"810e29a0-44c9-4c18-8d6b-e88a47fc6fa8"],
 "\nCombining (\[Star]) and (\[Star]\[Star]), we conclude\n  ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     FractionBox["1", 
      RowBox[{"3", "!"}]], 
     SuperscriptBox["\[Gamma]", "a"], 
     SuperscriptBox["\[Gamma]", "b"], 
     SuperscriptBox["\[Gamma]", "c"], 
     SuperscriptBox[
      SubscriptBox["\[Epsilon]", "abc"], "e"]}], "=", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["\[ImaginaryI]\[Gamma]", "5"]}], 
      SuperscriptBox["\[Gamma]", "e"]}], "=", 
     RowBox[{
      RowBox[{"+", " ", "\[ImaginaryI]"}], " ", 
      SuperscriptBox["\[Gamma]", "e"], 
      SuperscriptBox["\[Gamma]", "5"]}]}]}], TraditionalForm]],
  ExpressionUUID->"6de6ed90-2a64-4d7d-890a-e1e0eb4824d7"],
 "\nor simply\n  ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      SuperscriptBox["\[Gamma]", "5"], ",", 
      SuperscriptBox["\[Gamma]", "a"]}], "}"}], " ", "=", " ", "0"}], 
   TraditionalForm]],ExpressionUUID->"1df2dfd5-3d1b-4ff1-8e59-9f0d00d6dd77"],
 "."
}], "Text",ExpressionUUID->"91132ca2-bec2-4a81-852e-9cbe75942d07"],

Cell[TextData[{
 "Now instead of dealing with the many indices of ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox["\[ImaginaryI]", 
     RowBox[{"4", "!"}]], 
    SubscriptBox["\[Epsilon]", "abcd"], 
    SuperscriptBox["\[Gamma]", "a"], 
    SuperscriptBox["\[Gamma]", "b"], 
    SuperscriptBox["\[Gamma]", "c"], 
    SuperscriptBox["\[Gamma]", "d"]}], TraditionalForm]],ExpressionUUID->
  "b03e6790-f37d-4e06-a6d4-3bbdd072ad83"],
 ", we can define an abstract object ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["\[Gamma]", "5"], TraditionalForm]],ExpressionUUID->
  "c60ffc1d-f533-4d22-a7c5-bf43e1462552"],
 " and add it to our algebra. All the relations involve only anticommutators, \
so it makes sense to make this have an odd grade."
}], "Text",ExpressionUUID->"a0c93cf8-2c6a-4a8a-b819-bcf28bb534a6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefTensor", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", "M", ",", 
   RowBox[{"GradeOfTensor", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"AP", "\[Rule]", "1"}], "}"}]}], ",", 
   RowBox[{
   "PrintAs", "\[Rule]", 
    "\"\<\!\(\*SuperscriptBox[\(\[Gamma]\), \(5\)]\)\>\""}]}], "]"}]], "Input",
 CellLabel->"In[68]:=",ExpressionUUID->"b67532ab-3d5e-473c-a81c-113f9ea91d8d"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"\[Gamma]5", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`\[Gamma]5[], ". ", ""],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[68]:=",ExpressionUUID->"d7335524-3f37-49f6-ae41-65fc54db3fe9"]
}, Open  ]],

Cell["Add to AlgebraElements and AlgebraStructure", \
"Text",ExpressionUUID->"f656cda3-c615-4142-8d60-bf9cdbe32a02"],

Cell[BoxData[
 RowBox[{
  RowBox[{"AlgebraElements", "=", 
   RowBox[{"{", 
    RowBox[{"\[Gamma]", ",", "\[Gamma]5"}], "}"}]}], ";"}]], "Input",
 CellLabel->"In[69]:=",ExpressionUUID->"306652d8-cc0b-4483-9dee-39ed96f2558c"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"AlgebraStructure", "[", 
   RowBox[{"\[Gamma]", ",", "\[Gamma]5"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Supercommutator", "[", "AP", "]"}], "[", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "i", "]"}], ",", 
     RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "\[Equal]", 
   "0"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"AlgebraStructure", "[", 
   RowBox[{"\[Gamma]5", ",", "\[Gamma]5"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Supercommutator", "[", "AP", "]"}], "[", 
    RowBox[{
     RowBox[{"\[Gamma]5", "[", "]"}], ",", 
     RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "\[Equal]", "2"}]}]}], "Input",
 
 CellLabel->"In[70]:=",ExpressionUUID->"029305d9-70ed-4fbe-ba45-c7fbe1cf651f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Outer", "[", 
   RowBox[{
   "AlgebraStructure", ",", "AlgebraElements", ",", "AlgebraElements"}], 
   "]"}], "//", "TableForm"}]], "Input",
 CellLabel->"In[72]:=",ExpressionUUID->"6f5ffcd5-b75b-4e54-8cfe-44698e1104b6"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     RowBox[{
      InterpretationBox[
       StyleBox[
        SubscriptBox[
         RowBox[{"\[LeftDoubleBracket]", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"i"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`i],
           Editable->False], ",", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"j"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`j],
           Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xTensor`Supercommutator[$CellContext`AP][
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma][$CellContext`j]],
       Editable->False], "\[Equal]", 
      RowBox[{"2", " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"g", 
            StyleBox[GridBox[{
               {"i", "j"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->Rational[39, 4]]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`g[$CellContext`i, $CellContext`j],
        Editable->False]}]}], 
     RowBox[{
      InterpretationBox[
       StyleBox[
        SubscriptBox[
         RowBox[{"\[LeftDoubleBracket]", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"i"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`i],
           Editable->False], ",", 
          InterpretationBox[
           StyleBox[
            SuperscriptBox["\[Gamma]", "5"],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma]5[],
           Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xTensor`Supercommutator[$CellContext`AP][
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma]5[]],
       Editable->False], "\[Equal]", "0"}]},
    {
     RowBox[{
      InterpretationBox[
       StyleBox[
        SubscriptBox[
         RowBox[{"\[LeftDoubleBracket]", 
          InterpretationBox[
           StyleBox[GridBox[{
              {"\[Gamma]", 
               StyleBox[GridBox[{
                  {"i"},
                  {" "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->Rational[39, 4]]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma][$CellContext`i],
           Editable->False], ",", 
          InterpretationBox[
           StyleBox[
            SuperscriptBox["\[Gamma]", "5"],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma]5[],
           Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xTensor`Supercommutator[$CellContext`AP][
        $CellContext`\[Gamma][$CellContext`i], 
        $CellContext`\[Gamma]5[]],
       Editable->False], "\[Equal]", "0"}], 
     RowBox[{
      InterpretationBox[
       StyleBox[
        SubscriptBox[
         RowBox[{"\[LeftDoubleBracket]", 
          InterpretationBox[
           StyleBox[
            SuperscriptBox["\[Gamma]", "5"],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma]5[],
           Editable->False], ",", 
          InterpretationBox[
           StyleBox[
            SuperscriptBox["\[Gamma]", "5"],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`\[Gamma]5[],
           Editable->False], "\[RightDoubleBracket]"}], "\[Diamond]"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xTensor`Supercommutator[$CellContext`AP][
        $CellContext`\[Gamma]5[], 
        $CellContext`\[Gamma]5[]],
       Editable->False], "\[Equal]", "2"}]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellLabel->
  "Out[72]//TableForm=",ExpressionUUID->"288ea43c-7a30-4eaf-89b8-e80da94f3c3a"]
}, Open  ]],

Cell["So we have the following rule:", \
"Text",ExpressionUUID->"4a6af408-a4ff-41ae-87e6-427edce7f648"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"CommuteAlgebraRule", "[", "AlgebraStructure", "]"}], "[", 
  RowBox[{"AP", "[", 
   RowBox[{
    RowBox[{"\[Gamma]5", "[", "]"}], ",", 
    RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "]"}]], "Input",
 CellLabel->"In[73]:=",ExpressionUUID->"c20ef355-bc0e-41de-b5fa-f72cff844414"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"HoldPattern", "[", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       InterpretationBox[
        StyleBox[
         SuperscriptBox["\[Gamma]", "5"],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma]5[],
        Editable->False], "\[Diamond]", 
       InterpretationBox[
        StyleBox[
         SuperscriptBox["\[Gamma]", "5"],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`\[Gamma]5[],
        Editable->False]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AP[
      $CellContext`\[Gamma]5[], 
      $CellContext`\[Gamma]5[]],
     Editable->False], "]"}], "\[RuleDelayed]", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", "}"}], ",", "1"}], "]"}]}], "}"}]], "Output",
 CellLabel->
  "Out[73]=",ExpressionUUID->"035ad222-3f71-49c5-9f64-e78609c10e20"]
}, Open  ]],

Cell["Make it automatic.", \
"Text",ExpressionUUID->"ea42287a-2daa-44ab-83f5-bd0ec3c2cdcc"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AutomaticRules", "[", 
  RowBox[{"\[Gamma]5", ",", 
   RowBox[{
    RowBox[{"CommuteAlgebraRule", "[", "AlgebraStructure", "]"}], "[", 
    RowBox[{"AP", "[", 
     RowBox[{
      RowBox[{"\[Gamma]5", "[", "]"}], ",", 
      RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "]"}]}], "]"}]], "Input",
 CellLabel->"In[74]:=",ExpressionUUID->"fcc1819e-fc66-493c-b1ff-2cb4700618cc"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"   Rules \"\>", "\[InvisibleSpace]", 
   RowBox[{"{", "1", "}"}], 
   "\[InvisibleSpace]", "\<\" have been declared as UpValues for \"\>", 
   "\[InvisibleSpace]", "\[Gamma]5", "\[InvisibleSpace]", "\<\".\"\>"}],
  SequenceForm["   Rules ", 
   Shallow[{1}], 
   " have been declared as UpValues for ", $CellContext`\[Gamma]5, "."],
  Editable->False]], "Print",
 CellLabel->
  "During evaluation of \
In[74]:=",ExpressionUUID->"5186b3b0-77f2-4706-9b8d-678c97ff1116"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", 
   RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}]], "Input",
 CellLabel->"In[75]:=",ExpressionUUID->"fbac9993-98c3-4e64-b73e-cbb3daa53d47"],

Cell[BoxData["1"], "Output",
 CellLabel->
  "Out[75]=",ExpressionUUID->"c0c8374b-18fc-4cc2-86b4-52da9ce7cd03"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
 "9. Simple examples including ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["\[Gamma]", "5"], TraditionalForm]],ExpressionUUID->
  "63349938-78d1-4672-88da-3a046c91a5db"]
}], "Subsubsection",ExpressionUUID->"a2b10ebd-b9b9-4fc9-8a92-c38207b8f001"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "a", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}]}], "Input",
 CellLabel->"In[76]:=",ExpressionUUID->"303c2545-347a-48bd-845b-ee6e415b8ed6"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma]5[], 
   $CellContext`\[Gamma][$CellContext`a]],
  Editable->False]], "Output",
 CellLabel->"Out[76]=",ExpressionUUID->"d9b6a7f7-ff67-46db-a60d-bdac1115e03c"],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{"(", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[
        SuperscriptBox["\[Gamma]", "5"],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma]5[],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma]5[]],
    Editable->False], ")"}]}]], "Output",
 CellLabel->
  "Out[77]=",ExpressionUUID->"c9937b46-6aac-46bf-8909-8b41a24d52e7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}]}], "Input",
 CellLabel->"In[78]:=",ExpressionUUID->"07d4e10f-c93a-4b3c-964c-0b17f1718147"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma]5[], 
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma]5[]],
  Editable->False]], "Output",
 CellLabel->"Out[78]=",ExpressionUUID->"8db26d88-af44-491a-b724-44746d3b1d4c"],

Cell[BoxData[
 RowBox[{"-", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"\[Gamma]", 
       StyleBox[GridBox[{
          {"a"},
          {" "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`\[Gamma][$CellContext`a],
   Editable->False]}]], "Output",
 CellLabel->
  "Out[79]=",ExpressionUUID->"723e5b2f-1610-4a78-b5ec-b97fb820cbe2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
   RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}]}], "Input",
 CellLabel->"In[80]:=",ExpressionUUID->"1cb4cd4d-d88e-48cb-8cd7-085e155218c1"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma]5[], 
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b], 
   $CellContext`\[Gamma]5[]],
  Editable->False]], "Output",
 CellLabel->"Out[80]=",ExpressionUUID->"3ed10623-f806-4a78-9689-f2789057b586"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b]],
  Editable->False]], "Output",
 CellLabel->
  "Out[81]=",ExpressionUUID->"9469ebec-0ade-4e9a-9d6e-291ec302d7a2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"AP", "[", 
  RowBox[{
   RowBox[{"\[Gamma]5", "[", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "a", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "b", "]"}], ",", 
   RowBox[{"\[Gamma]", "[", "c", "]"}], ",", 
   RowBox[{"\[Gamma]5", "[", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "mySAP"}]}], "Input",
 CellLabel->"In[82]:=",ExpressionUUID->"5ca84513-90f8-4463-9a58-1fb769fa82ad"],

Cell[BoxData[
 InterpretationBox[
  StyleBox[
   RowBox[{
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"a"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`a],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"b"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`b],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Gamma]", 
         StyleBox[GridBox[{
            {"c"},
            {" "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->Rational[39, 4]]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma][$CellContext`c],
     Editable->False], "\[Diamond]", 
    InterpretationBox[
     StyleBox[
      SuperscriptBox["\[Gamma]", "5"],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`\[Gamma]5[],
     Editable->False]}],
   ShowAutoStyles->False,
   AutoSpacing->False],
  $CellContext`AP[
   $CellContext`\[Gamma]5[], 
   $CellContext`\[Gamma][$CellContext`a], 
   $CellContext`\[Gamma][$CellContext`b], 
   $CellContext`\[Gamma][$CellContext`c], 
   $CellContext`\[Gamma]5[]],
  Editable->False]], "Output",
 CellLabel->"Out[82]=",ExpressionUUID->"ead1eafc-f049-4581-b2c5-d1749c95b7a1"],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{"(", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"a"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`a],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"b"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`b],
       Editable->False], "\[Diamond]", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Gamma]", 
           StyleBox[GridBox[{
              {"c"},
              {" "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->Rational[39, 4]]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`\[Gamma][$CellContext`c],
       Editable->False]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AP[
     $CellContext`\[Gamma][$CellContext`a], 
     $CellContext`\[Gamma][$CellContext`b], 
     $CellContext`\[Gamma][$CellContext`c]],
    Editable->False], ")"}]}]], "Output",
 CellLabel->
  "Out[83]=",ExpressionUUID->"6693fb21-5b97-43f4-ba8b-85757d61c961"]
}, Open  ]],

Cell["\<\
We can always replace \[Gamma]5\[Rule]\[Gamma]5Explicit to perform explicit \
calculations:\
\>", "Text",ExpressionUUID->"f03af937-318d-434a-a429-8fbba6fef127"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"-", "\[ImaginaryI]"}], " ", 
  RowBox[{"epsilong", "[", 
   RowBox[{"d", ",", "a", ",", "b", ",", "c"}], "]"}], 
  RowBox[{"AP", "[", 
   RowBox[{
    RowBox[{"\[Gamma]5", "[", "]"}], ",", 
    RowBox[{"\[Gamma]", "[", 
     RowBox[{"-", "d"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"%", "/.", 
      RowBox[{"{", 
       RowBox[{"\[Gamma]5", "\[Rule]", "\[Gamma]5Explicit"}], "}"}]}], "//", 
     "ToCanonical"}], ")"}], "/.", "\[Gamma]\[Gamma]ContractRule"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"%", "//", "mySAP"}], "//", "ContractMetric"}], ")"}], "//.",
        "\[Gamma]\[Gamma]ContractRule"}], "//", "mySAP"}], "//", 
     "ContractMetric"}], ")"}], "//.", "\[Gamma]\[Gamma]ContractRule"}], "//",
   "ToCanonical"}]}], "Input",
 CellLabel->"In[84]:=",ExpressionUUID->"7bbc32f7-fcdb-4403-a3b3-b24196afdd02"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "\[ImaginaryI]"}], " ", 
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[
       SuperscriptBox["\[Gamma]", "5"],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma]5[],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {" "},
             {"d"}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][-$CellContext`d],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma]5[], 
    $CellContext`\[Gamma][-$CellContext`d]],
   Editable->False], " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"\[Epsilon]g", 
       StyleBox[GridBox[{
          {"d", "a", "b", "c"},
          {" ", " ", " ", " "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->Rational[39, 4]]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`epsilong[$CellContext`d, $CellContext`a, $CellContext`b, \
$CellContext`c],
   Editable->False]}]], "Output",
 CellLabel->"Out[84]=",ExpressionUUID->"0e0122aa-9658-4714-8185-96b79eb7ff35"],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"a"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`a],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"b"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`b],
      Editable->False], "\[Diamond]", 
     InterpretationBox[
      StyleBox[GridBox[{
         {"\[Gamma]", 
          StyleBox[GridBox[{
             {"c"},
             {" "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->Rational[39, 4]]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`\[Gamma][$CellContext`c],
      Editable->False]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`AP[
    $CellContext`\[Gamma][$CellContext`a], 
    $CellContext`\[Gamma][$CellContext`b], 
    $CellContext`\[Gamma][$CellContext`c]],
   Editable->False], "-", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"b", "c"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`b, $CellContext`c],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"a"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`a],
    Editable->False]}], "+", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"a", "c"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`a, $CellContext`c],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"b"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`b],
    Editable->False]}], "-", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`g[$CellContext`a, $CellContext`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Gamma]", 
        StyleBox[GridBox[{
           {"c"},
           {" "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->Rational[39, 4]]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`\[Gamma][$CellContext`c],
    Editable->False]}]}]], "Output",
 CellLabel->
  "Out[86]=",ExpressionUUID->"2d7628d9-92be-449e-987b-e3909cf2028a"]
}, Open  ]]
}, Closed]]
}, Open  ]]
},
WindowSize->{1150, 644},
WindowMargins->{{Automatic, 62}, {Automatic, 62}},
PrivateNotebookOptions->{"FileOutlineCache"->False},
TrackCellChangeTimes->False,
FrontEndVersion->"11.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2018)",
StyleDefinitions->"Default.nb"
]
